I always thought that the general consensus was that the linked BS38s (1976-79) were hands-down the best, and I'm a little surprised that the gurus who have responded have not supported this. Anyways, I have re-built plenty of both sets, and here is why I like the BS38s best:
The BS38's have an adjustable slide needle, BS34s do not. This seems like a serious oversight to me. A lot of us believe that the BS34s were a response to EPA requirements, and were never intended to be tampered with, and that Mikuni built them accordingly.
It is very easy to adjust the air mix screw on a running BS38. On a BS34 you first have to drill out the air mix screw cap, and even then, it is very awkward to adjust the screw, and you burn your hand on the engine while trying to do so. See the EPA comment above.
The main jet of a BS38 can be changed without removing the float bowl. The pilot jet of a BS38 is in the float bowl, so it is also very easy to change. Replacing either jet on a mounted BS34 is more awkward.
BS38s look better. The stamped metal diaphragm caps on BS34s are cheesy-looking and the chrome will eventually rust and pit. The caps on BS38s are cast aluminum, look great, and can always be polished to a mirror finish. The rest of the BS38 body looks better too in my opinion, better curves and lines. Plus, a lot of BS34s are painted black, which eventually chips and wears and fades and looks ratty.
The one significant advantage of the BS34s is that the choke (actually an enrichener) is adjustable. The BS38 choke is either all on or all off.
Also, the BS34 float valve has a screen which the BS38 doesn't, but you should be running an in-line fuel filter, so this shouldn't matter.
Also, on the 1978-79 BS38s you need a special tool to get to the slide needle.